Z. Kharebava

On a Multiplicativity up to Homotopy of the Gugenheim Map

In the category of differential algebras there is a Gugenheim's strongly homotopy multiplicative map r: A C from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both BA and BC carry multiplications. We show that the Gugenheim's map Br: BABC is multiplicative up to homotopy with respect to these products.